【正文】 ation may have several ponents, some of which may be frequencydependent and some frequencyindependent. The total attenuation is the sum of the contributions of all in?uencing factors [14], and this relationship applies to both bulk waves and guided waves: (2)where is the attenuation coef?cient of the ith ponent caused by the ith factor, is the travel distance affected by the ith factor, is the amplitude ratio after attenuation of the ith ponent, If is the same for all factors, then wehave or (3)where is the total attenuation coef?cient.According to the cause, attenuation may be grouped into the following categories:(a) Dissipative attenuation: An energy loss due to nonelastic resistance of the medium. It increases with thewave travel distance and may bee profound over a long distance depending on the material property. This type of attenuation in steel is generally very low pared to that in rocks. As shown later, it can beignored in practice for guided waves traveling in rock bolts due to the low resistance of steel and the short bolt length (1–3 m).(b) Dispersive attenuation: An energy loss due to deformation of waveform during wave propagation, a characteristic that distinguishes guided waves from bulk waves. The phenomenon of wave deformation is calledenergy dispersion.(c) Spreading attenuation: An energy loss which occurs at the interface between the bolt and the grouting material. As a guided wave reaches the interface, not all of the wave energy can be re?ected at the interface. Part of the energy passes through the interface and is transmitted into the grouted material, a phenomenon called energy leakage.Therefore, it can be reasonably assumed that attenuation in grouted rock bolts consists of two major ponents。 at frequencies higher than 75 kHz the velocity increase in the grouted bolts slowed down, and at the highfrequency end (., 100 kHz), the velocity was approaching that of the free bolts. In fact, at high frequencies, it was more dif?cult to separate the grouted length and the free length from the recorded signals. Therefore, frequencies higher than 75 kHz are not remended for the test.6. Discussions and conclusionsThis research examined the attenuation and group velocity of the guided ultrasonic waves in rock bolts. The test results showed variations with frequency and grouted length. It was determined that due to the short length of rock bolts used in the ?eld, the dissipative attenuation can be ignored.In free bolts, the dispersive and spreading attenuation along the bolt is negligible and the main source of attenuation is from the setup loss of energy, which reduced the amplitude by 20% in one round trip for the equipment setup in this research. The setup loss is considered to be independent from frequency and bolt length, but dependent upon the speci?c equipment setup. The group velocityin the free bolts decreased by about 10% as the frequency increased from 25 to 100 kHz.In grouted bolts, the setup loss is assumed to be the same as that in the free bolts because the test setup was the same. However, the dispersive and spreading (DISP) attenuation increased with frequency and grouted length, and it was moresevere than that from the setup loss. The amplitude ratio due to the DISP attenuation decreased as the frequency and grouted length increased. The group wave velocity in the grouted length of the test bolts increased steadily as the frequency increased to 75 kHz while the increase slowed down at a higher frequency. However, at 25 kHz, the group velocity wasnearly 50% lower in the grouted length than that in the free bolts. As the frequency approached 100 kHz, the velocity difference between the free bolts and the grouted length was reduced to less than 10%.As indicated earlier, the experiments in this study were conducted using a transmissionthrough setup (., with sensors on both ends of the tested bolts). This type of setup is not applicable to the ?eld where only one end of a rock bolt is accessible. The next step of this research will be to conduct similar tests using a transmissionecho setup (., with a sensor at one end only). This will require a different testing device, which is being custombuilt for the speci?c testing requirements. During the next stage of research, tension will also be applied to the bolt samples to study the tension effects. The ultimate goal of this research will be to develop a nondestructive testing device using guided ultrasonic waves for ?eld monitoring of grouted rock bolts, particularly the grout quality, grouted length, bolt failure, and bolt tension.AcknowledgmentsThis research was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada.中文譯文頻率和錨固長度對超聲波在錨桿中傳播行為的影響. Zoua, Y. Cui, V. Madengaa, C. Zhang摘要以頻率從25至100千赫的超聲波作為勵磁輸入，研究超聲波在自由和錨固錨桿中傳播的特性。在自由錨桿中，波的衰減不受錨桿長度和波頻的影響。在許多應(yīng)用中，錨桿用水泥或樹脂錨固。用拉拔實驗結(jié)果來衡量錨固質(zhì)量，受錨桿初次破壞后關(guān)鍵錨固長度的限制。雖然超聲導(dǎo)波是一個很有前景的監(jiān)測錨桿的方法，但是在這一領(lǐng)域的研究仍尚處于初期階段，許多技術(shù)問題仍待解決。群速度決定其傳播速度，波整體以該速度傳播。頻率越低，速度越低。一般來說，衰減是指信號強度的減弱。舉例來說，縱波振幅衰減可以表示為一個距離函數(shù)。這些因素都可能造成一些衰減。它隨波的傳播距離的增加而增加，并可能根據(jù)物質(zhì)的性質(zhì)在長距離傳播時成為很顯著的原因。這種波變形的現(xiàn)象稱為能量色散。因此，可以合理地假設(shè)在錨固錨桿中衰減由兩部分組成:色散衰減和傳播衰減，這兩者都是跟頻率密切相關(guān)的。理論上說，當一個波到達毗鄰另一不傳送機械波的界面（例如真空或空氣），沒有折射發(fā)生，所有能量都被反射回去。結(jié)果表明，記錄的此類振幅衰減和能量損失在錨桿測試中將大于真正由色散衰減所致。2 超聲導(dǎo)波測試的實驗了解超聲波在自由錨桿（非錨固）中的特點 ，是研究超聲導(dǎo)波在錨固錨桿中行為所必不可少的。錨固錨桿在現(xiàn)場是用圓柱混凝土在鋼筋周圍砌成塊狀來模擬該錨固錨桿的(圖1)。3個具有不同錨固長度的錨桿（試件3~5）被用來觀察頻率和錨固長度對導(dǎo)波衰減的影響。超聲波正弦輸入信號被用來激發(fā)在錨桿非錨固末端的發(fā)射機。兩端測試錨桿均是平滑的，真空潤滑脂被用來提供傳感器間的良好接觸。衰減估計是比較首次到達波和回聲的振幅比。據(jù)了解，好的錨固質(zhì)量由于能量泄漏及色散導(dǎo)致沿錨桿更高的能量損失。因此，建立一種有效的分析方法來分析超聲波的衰減和獲得有意義的結(jié)果非常關(guān)鍵。為了說明時間間隔的長度對結(jié)果準確度的影響，用不同時間間隔計算自由錨桿中的振幅比(首次到達和回聲的界限很明顯)，用百分比表示。下面的實驗都用t1=t2=100us的時間間隔來計算。 估算群速度從記錄錨桿輸入端的勵磁信號到錨桿另一端的首次到達之間的延時定義為波在錨桿中的傳播時間。在matlab中通過一個濾波程序就可以實現(xiàn)。根據(jù)錨桿長度和用這種方法確定的傳播時間，可以計算出超聲導(dǎo)波的群速度。由數(shù)據(jù)分析可看出，隨著輸入頻率的增加，首次到達的時間和回聲到達接收端的時間緩慢增加，而由首次到達產(chǎn)生的回聲的降幅在任何輸入頻率下都相同。由于傳播距離很短，所以錨桿中的色散衰減可以忽略。但是安裝損耗在每次不同的實驗中都不盡。對兩個自由錨桿的能量損失不隨頻率和錨桿長度而變化，